Ruin Theory
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Fehr, Ashley
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Abstract
Classical ruin theory was developed by Lundberg in 1907 and refined by Cramer in 1930. This theory describes the evolution of the surplus of an insurance company over time. It assumes that an insurance company begins with an initial surplus and then receives premiums continuously at a constant rate. It also assumes that claims of random and independent size are paid at random and independent times. Ruin occurs when the surplus becomes negative meaning that the average inflow of money (premiums) is smaller than the average outflow of money (claims). Cramer expanded on this theory to show that probability of ruin decays exponentially fast as the initial surplus grows larger. This paper will synthesize some of the key results from Ruin Theory. These results will not be proven via formula but will be conclusively demonstrated using simulation.
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Keywords
Ruin Theory, Compound Poisson, Adjustment coefficient, Monte Carlo